The invention relates to a device for measuring the angle of rotation and including two bodies having areas of electrically conductive and/or ferromagnetic material, and sensor coils whose resistance changes as a function of change in the magnitude of area of one of the bodies assigned to sensor coils. In a known measuring device the rotation of a shaft is determined by two concentrically arranged sleeves which are moved relative to one another. One of the sleeves comprises two rows of slots which are offset relative to one another and form the electrically nonconductive area. In the other sleeve, a row of continuous slots is formed which likewise extend in the direction of the sleeve axis. At least one coil, through which a high-frequency alternating current flows, is arranged in the area of the two slot rows of the first sleeve. The electrically nonconductive surface of the sleeves, i.e. the opening surface of the slots, is changed by relative tangential displacement of the two sleeves relative to one another, so that the damping of the coils is varied. The measuring device has the disadvantage that only small angles of rotation are measurable.